Depending on the severity there are materials you can get right from your auto parts store that will work as well as anything else.
For starts you can try Meguiar's X 2.0 Fine Scratch and Blemish Remover which works equally well both on auto paint and poly finished guitars.
If there are many scratches that are smaller and are starting to produce a haze like area around switches and knobs use Zymol. Look for the blue bottle. This is both a cleaner and a wax and it will surprise you. It's not cheap, but it's amazing how well it works.
Good luck!

Anything that works well for cars will work great for guitars. I use the 3M products on both for scratch removal and a good polymer "wax" after. The polymer finish is so strong they will protect the surface a lot of damage down the road.

ZYMOL!!! Original Zymol is the best. It cleans as well as polishes and you would think you have a brand-new guitar or bass. Actually, it should be used immediately upon purchasing a new guitar or bass in order to complete the cleaning, polishing, protecting, and removal of rubbing compound traces so the instrument will look its best for years to come.

Here's the word from the man himself, Mr. Bennett, CEO of Zymol:

Hello All, I'm Chuck Bennett, CEO of Zymol and a Bass Player for 43 years. I am interested in answering questions but NOT selling product. I don't have my very old Gibson Ripper anymore because my son, who is a better bass player than I am, fell in love with the bass and received it as a birthday gift! I can't promise I will be able to answer technical finish questions on a timely basis but I will do my best. As for the question about what to wipe a guitar or bass with, be VERY careful! We use T-shirts to micro-sand automobile finishes. Never, ever use a diaper. Microwipes are great as long as you use the wipes that are composed of Nylon and Nitrile, not Polyester and Polyamide. This 'rubber' based compound will not scratch. Nitrocellulose finishes are beautiful, in fact you can't use Nitrocellulose on cars anymore due to the level of VOC's because they scratch just looking at them. Knowing what your finish is made of is the first step in caring for it!

For really deep scratches you may have to wet sand and then buff it out. (Warning .. you can really screw up a finish this way if you don't know what you are doing .. try it on a cheap bass or guitar.)

I use "Gerlitz" No1 carnauba wax & polish. its the best guitar polish i have used in my 45 years of playing bass.
it's the only thing I put my my bass other than lem oil for the fretboards, The gerlitz is really good and in a few minuets you get a really deep polish and shine. even cover light scratches. really recommend this polish.

yes but make sure it is not lacquered as it can react with some lacquers, also would only do it once a year or longer as over time it could darken the maple a little. I have used it on my Artisan lead guitar with a maple fretboard and it make the Maple look more golden after a few years.

Depending on the severity there are materials you can get right from your auto parts store that will work as well as anything else.
For starts you can try Meguiar's X 2.0 Fine Scratch and Blemish Remover which works equally well both on auto paint and poly finished guitars.
If there are many scratches that are smaller and are starting to produce a haze like area around switches and knobs use Zymol. Look for the blue bottle. This is both a cleaner and a wax and it will surprise you. It's not cheap, but it's amazing how well it works.
Good luck!